Phase discrimination for micro electrical measurement in non-conductive fluid

ABSTRACT

A method for electrically investigating a wall of a borehole in a geologic formation including injecting a current into the formation at a first position along the wall and returning the current at a second position along the wall, the formation current having a frequency below about 100 kHz, measuring a voltage in the formation between a third position and a fourth position along the wall, the third and fourth positions being located between the first and second positions, and determining an amplitude of a component of the voltage in phase with the current.

BACKGROUND OF INVENTION

1. Field of the Invention

The invention relates generally to exploring for hydrocarbons usingelectrical investigation. More particularly, the invention relates to amethod and apparatus for discriminating against unwanted signals thatare dephased from the desired signal.

2. Background Art

When exploring a borehole drilled through an earth formation, it isdesirable to know the characteristics of the geologic formation atvarious depths of the borehole. These characteristics include thestratifications, non-homogenous elements, and the size and shape ofpores and breaks in the formation.

One technique for detecting these characteristics uses a tool with aseries of current electrodes located on the face of a conductive padthat is pressed against the wall of the borehole. A constant currentsource injects a measurement current into the formation through a sourceelectrode and returns the current through a return electrode situated onanother part of the pad. The pad is moved along the borehole wall, andthe discrete current signals associated with each electrode are relatedto the resistivity of the formation. If, however, a non-conductivedrilling fluid (“mud”) is used, such as an oil based mud or water-in-oilemulsion type mud, the resulting non-conductive mud layer between thepad and the wellbore wall produces poor and unusable signals.

Another technique can image a borehole drilled with a non-conductivemud. The tool for this technique uses a non-conductive pad with twocurrent injectors and an array of voltage electrodes. The two currentinjectors, a source electrode and a return electrode, inject a currentinto the formation, and the current passes through the formation in apath parallel to the pad. The voltage electrodes measure the voltagedifferential in the formation where the current is passing. Thismeasurement of the voltage is important because the resistivity of theformation is related to the voltage.

The resistivity of the formation can be calculated using the followingequation: $\begin{matrix}{\rho = \frac{E}{J}} & (1)\end{matrix}$where ρ is the resistivity of the formation, E is the electric field inthe formation, and J is the current density. The electric field E isgiven by the differential voltage δV divided by the voltage electrodeseparation, and the current density J is given by the current I dividedby a geometric factor g. Substituting for E and 3 in Equation 1 gives:$\begin{matrix}{\rho = {k\frac{\quad{\delta\quad V}}{I}}} & (2)\end{matrix}$where k is a geometric factor with units of length. Thus, theresistivity of a formation can be determined by injecting a current intothe formation, measuring a voltage, and computing the resistivity of theformation using Equation 2.

The prior art pad used in this method is shown in FIGS. 1A and 1B. Thepad is shown generally in FIG. 1 at element 1. It contains a sourceelectrode 2, a return electrode 3, and an array of pairs of voltageelectrodes 4. The pad 1 itself is constructed of a non-conductive,insulative material 5, such as ceramics or polymers, that have a highstrength, and high chemical and thermal stability.

The pad 1 is placed against the wall of a borehole 7, which may have amud cake layer 6. An electrical current is injected into the formation 8through the source electrode 2, returning at the return electrode 3. Thevoltage electrodes 4 measure a voltage in the formation 8, and theresistivity of the formation can be calculated using Equation 2, above.

When the pad 1 is not in contact with the borehole wall 7, the distancebetween the pad 1 and the borehole wall 7 is called “standoff.” Thereare three main standoff effects: (1) mud and pad signals, (2) currentleakage, and (3) voltage inaccuracies. There are various ways to reducethese effects so that accurate measurements can be made even when thepad 1 is not in direct contact with the borehole wall 7.

The current electrodes 2, 3 generate an electric field in the mud and inthe insulating pad 5 which is detected by the voltage electrodes 4. Onetool to reduce pad signal, shown in FIG. 9B, has a conductive backplate92 behind the insulating pad 5 and parallel to the front face of thetool 1. The backplate 92 is maintained at an electrical potential equalto that of the formation in front of the voltage electrodes 4. Thistechnique is described in Patent WO 0177711. This shields the array ofvoltage electrodes from the mud and pad signals.

“Current leakage” describes the condition when not all of the currentinjected from the source electrode 2 passes through the formation 8,referring to FIG. 1A. Ideally, when the pad 1 makes good contact withthe borehole wall 7, the injected current passes almost entirely throughthe formation 8. But when mud or a mud cake layer 6 lies under one orboth current electrodes 2, 3, when there is significant standoff, partof the current, called leakage current, will leak by capacitive couplingfrom the source electrode 2 to the return electrode 3, without passingthrough the formation 8. This situation is shown in the model circuit inFIG. 2.

FIG. 2 shows a current source 21 modeled to be in a parallel circuitwith a leakage impedance Z_(L) and a variable mud impedance Z_(M). Theformation current I_(F) passes through the impedance of the mud or mudcake layer and through the formation. The leakage current I_(L) passesthrough the leakage impedance Z_(L), but does not pass through theformation. When calculating the resistivity of the formation, theformation current must be used in Equation 2.

The leakage current I_(L) and the formation current I_(F) sum to thetotal current I. Thus, the formation current is given by:I _(F) =I−I _(L)  (3)Using Z=(V/I), the above equation can be transformed into a more usefulform: $\begin{matrix}{I_{F} = {I\left\lbrack {1 - \frac{Z_{INJ}}{Z_{L}}} \right\rbrack}} & (4)\end{matrix}$where Z_(INJ) is the total impedance seen by the injector circuit, asmeasured by the tool, and Z_(L) is the leakage impedance of the tool,which can be experimentally determined. Thus, the formation currentI_(F) can be computed from the injection voltage and current, withoutknowing the formation impedance Z_(F), standoff, or mud properties. Analternative method for determining the true current in the formation isto use injection electrodes 2,3 that are shielded by a conductive box,where the shields are maintained at the same electric potential as eachelectrode, as described in Patent WO 0177710.

Errors in the voltage measurement occur because the voltage electrodes 4couple not only to the formation but also to the conductive backplate.The voltage output from the electrodes is given by: $\begin{matrix}{{\delta\quad V} = {\delta\quad V_{TRUE}\frac{Z_{S}}{Z_{S} + Z_{C}}}} & (5)\end{matrix}$where δV_(TRUE) is the true voltage in the formation, Z_(S) is thecoupling impedance to the backplate and Z_(C) is the contact impedancebetween the voltage electrodes and the formation. A scalar correction isobtained by solving for δV_(TRUE): $\begin{matrix}{{\delta\quad V_{TRUE}} = {\delta\quad{V\left( {1 + \frac{Z_{C}}{Z_{S}}} \right)}}} & (6)\end{matrix}$

FIG. 4 is a diagram of an equivalent circuit showing the current flowusing the prior art tool. It is similar to FIG. 2, but shows more detailalong the path of the formation current I_(F). FIG. 4 shows the mudimpedance Z_(M) of FIG. 2 to be a series containing a mud impedance atthe upper or source electrode Z_(MU), a formation resistance R_(F), anda mud impedance at the lower or return electrode Z_(ML). Thus, theformation current flows through the formation resistance RF via the twomud impedances Z_(MU), Z_(ML).

To a first approximation, the contact impedance of a voltage electrodeZ_(C) is linearly proportional to the mean contact impedance of thecurrent injection electrodes: $\begin{matrix}{Z_{C} = {\left( \frac{Z_{MU} + Z_{ML}}{2} \right) \cdot \left( \frac{A_{INJ}}{A_{BUT}} \right)}} & (7)\end{matrix}$where A_(INJ) is the current injector 2, 3 area and A_(but) is thevoltage electrode 4 (button) area.

Because the mud impedances under the injectors Z_(MU), Z_(ML) areusually much greater than the impedance of the formation R_(F), V=IR canbe rewritten as: $\begin{matrix}{{Z_{MU} + Z_{ML}} \approx \frac{V}{I_{F}}} & (8)\end{matrix}$where I_(F) is given by Equation 4 and V is the voltage differenceacross the current electrodes 2, 3. Thus, δV_(TRUE) can be calculatedfrom V and I without knowing the standoff or mud properties.

FIGS. 3A and 3B show experimental resistivity data. FIG. 3A shows raw,uncorrected data in two different mud types, a 90/10 oil to water ratiomud and a 50/50 ratio mud, and with two different formations of mownresistivity, 20 Ω-m and 200 Ω-m Data with a conductive steel casing arealso shown. The casing data lines represent the signal in the mud andshows how the mud signal affects the measured resistivity as thestandoff increases. At large standoffs, the measured signal is composedalmost entirely of the mud signal and not the formation signal. FIG. 3Bshows the resistivity data after applying the scalar correction inEquations 4 and 6. The scalar corrected resistivity curves in the twoformations are more accurate in the range from no standoff to the pointon each curve where the mud signal becomes dominant, but at largestandoff the mud signal overwhelms the formation signal and the data areunusable.

SUMMARY OF INVENTION

One aspect of the invention is a method for electrically investigating awall borehole in a geologic formation that includes injecting a currentinto the formation at a first position on the wall, returning thecurrent at a second position on the wall, and measuring the voltagebetween a third and fourth position that are located between the firstand second positions. The method includes determining a component of thevoltage in phase with the current. In one embodiment, the invention alsoincludes calculating the formation resistivity based on the current andthe component of the voltage in phase with the current. In some otherembodiments, the invention includes applying a scalar correction for thecurrent leakage and voltage inaccuracies.

The well-logging tool according to the invention includes a pad adaptedto be placed into contact with a wall of a borehole, a source electrodelocated on the pad and adapted to inject an electrical current into theformation, a return electrode also located on the pad and adapted toreceive the current injected by the source electrode, an ammeteroperatively coupled to the electrode circuit, at least one pair ofvoltage electrodes located on the front face of the pad in between thesource and return electrodes, and a phase sensitive detector operativelycoupled to the voltage electrodes and adapted to measure an amplitude ofa component of the voltage in phase with the electrical current. In oneembodiment the pad is comprised of a non-conductive material and has aconductive back plate disposed on the back face of the pad. Otheraspects and advantages of the invention will be apparent from thefollowing description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A shows a cross-section of a prior art tool in contact with theformation.

FIG. 1B is a view of the face of the tool shown in FIG. 1A.

FIG. 2 is a circuit diagram of a model used in the prior art.

FIG. 3A shows a graph of raw resistivity data.

FIG. 3B is a graph of resistivity data after a prior art scalarcorrection.

FIG. 4 is a model circuit diagram showing the path of the current usingthe prior art tool.

FIG. 5 is a graph that shows the dephasing of the voltage relative tothe formation current as a function of standoff.

FIG. 6 is a graph of resistivity data using the component of the voltagein phase with the total current and using a scalar correction.

FIG. 7 is a flow chart showing an embodiment of the method according tothe invention.

FIG. 8 is a flow chart showing another embodiment of the methodaccording to the invention.

FIG. 9A shows the tool according to the invention with a phase sensitivemeasuring device.

FIG. 9B shown the tool with a conductive backplate.

DETAILED DESCRIPTION

The present invention includes a new method and apparatus fordiscriminating against unwanted signals when making microeletricinvestigations of a borehole wall. The invention is based on theelectric properties exhibited by the materials near the voltageelectrodes, when the frequency of the alternating current source isbelow about 100 kHz.

First, below about 100 kHz, most geologic formations can be treated aspurely resistive materials. That is, the electrical permittivity of theformation can be neglected:σ>>2πfε₀ε_(r)  (9)where σ is the conductivity of the formation, f is the frequency of theinjected alternating current, ε₀ is the permittivity of free space, andε_(r) is the relative permittivity of the formation.

Second, below about 100 kHz, the insulating materials surrounding thecurrent electrodes can be treated as pure dielectrics. That is, theconductivity of the insulating materials can be neglected.2πfε₀ε_(r)>>σ  (10)

Finally, the drilling mud can be treated as a leaky dielectric with:2πfε₀ε_(r)>σ  (11)or2πfε₀ε_(r)≈σ  (12)

Because of the dielectric nature of the drilling mud and the insulators,all of the impedances shown in FIG. 4 are complex impedances equivalentto parallel combinations of resistors and capacitors, where thecapacitive part is dominant. As a result, while the potential differencegenerated in the formation will be in phase with the formation currentI_(F), the potential differences generated in the leakage paths, becauseof the capacitive nature of the leakage impedances, will be dephasedfrom the formation current by an angle between 0° and −90°.

Using this phenomenon, the formation signal can be partiallydiscriminated from the fluid and insulator signals. This can be achievedusing the following equation:δV_(phase)=δV·cos(φ_(F))  (13)where φ_(F) is the phase of the voltage δV with respect to the formationcurrent I_(F). The formation current and its phase can be measured usingshielded current injectors, as described in the Background and Patent WO017710, or they can be calculated based on the equivalent circuit inFIG. 4, by independently measuring the leakage impedance Z_(L) andassuming it to be constant.

Further, experimental data have shown that for practical purposes, it issufficient to measure the phase of the total current I and use thecomponent of the voltage δV in phase with the total current. This, theabove equation simplifies to:δV_(phase)=δV·cos(φ)  (14)where φ is the phase of δV with respect to the total current I.

FIG. 5 shows the measured phase of the voltage δV relative to theformation current I as a function of standoff. As with FIGS. 3A and 3B,the graph in FIG. 5 shows data for two different mud types and twodifferent formation resistivities, along with data for a conductivesteel casing. At zero standoff the phase is close zero, indicating noleakage. (On the casing, the phase at small standoffs is not zerobecause of noise). At a large standoff, the phase is −90°, indicatingmainly leakage. A comparison of FIGS. 3A and 5 shows that a phase angleof −45° corresponds to the critical point where the calculatedresistivity begins to increase as a result of the mud and pad signalsbecoming significant compared to the formation signal.

Additionally, the phase correction can be used with the scalarcorrection described in the Background. Using Equation 2 above, aresistivity can be calculated with a scalar correction, ρ_(cor):$\begin{matrix}{\rho_{cor} = {{ak}\quad\frac{\delta\quad V}{I}}} & (15)\end{matrix}$where a, a function of (V/I), is the correction factor derived fromtheoretical modeling or experiments, as outlined in patent WO 0177710.

As an example, ρ_(cor) can be calculated as follows: $\begin{matrix}{\rho_{cor} = {k\quad\frac{\delta\quad V_{TRUE}}{I_{F}}}} & (16)\end{matrix}$where I_(F) is given by Equation 4 and δV_(TRUE) by Equation 6. Thephase correction can then be applied to the corrected resistivity toobtain a corrected phase resistivity, ρ_(cph):ρ_(cph)=ρ_(cor)·cos(φ)  (17)where φ is the phase of δV with respect to the total current I.

FIG. 6 shows the corrected phase resistivity according to the inventionas a function of standoff. Advantageously, the rapid rise in measuredresistivity caused by the pad and mud signals is attenuated, and theworking zone of the tool is extended to greater standoffs.

FIG. 7 shows the method according to the invention. Various principlesdiscussed above are applied in several embodiments of the invention.

First, an alternating current with a frequency below about 100 kHz isinjected into a formation, as shown in FIG. 7 at 71. The current isinjected at a first position along the borehole wall and returns at asecond position along the borehole wall. In some embodiments, the firstand second position correspond to the positions of the source and returnelectrodes on the pad.

Next, a voltage is measured between a third position and a fourthposition along the borehole wall, the third and fourth positions beinglocated between the first and second positions 72. In some embodimentsthe third and fourth positions correspond to the positions of thedifferential electrodes on the pad.

The method then includes determining the amplitude of a component of thevoltage that is in phase with the current 73. After determining theamplitude of the in phase component, the method includes calculating theresistivity of the formation 74, as shown in Equation 2. In someembodiments, the method includes determining a component of the voltagethat is in phase with a formation current. The formation current isdetermined by subtracting a leakage current calculated using anexperimentally determined leakage impedance.

In some embodiments, a scalar correction is applied for leakage andvoltage inaccuracies 75. These corrections, shown in Equations 4 and 6,make the resistivity calculations more accurate in the range betweenzero standoff and the point where mud signal becomes dominant.

FIG. 8 shows yet another embodiment of the invention, wherein thedetermining of the in phase component is performed on previouslyrecorded data. The embodiment includes determining the amplitude of acomponent of the recorded voltage in phase with the recorded current 81.The resistivity of the formation can then be calculated 82 using theabove equations. Again, a scalar correction can be applied 83 to makethe resistivity calculations more accurate between zero standoff and thepoint where the mud signal becomes dominant. In some embodiments, themethod includes determining the magnitude of a component of the voltagethat is in phase with the formation current.

A well-logging tool according to the invention is shown schematically inFIGS. 9A & 9B. In FIG. 9A the tool 1 is similar to the prior art tool inFIG. 1 in that it has a source electrode 2, a return electrode 3, andvoltage electrodes 4 located between the source 2 and return 3electrodes. The tool according to the invention also has an ammeter 95operatively connected to the source and return electrode circuit, theammeter being adapted to measure the total current. The tool 1 also hasa phase sensitive detector 91 that is adapted to measure the amplitudeof the voltage that is in phase with the current, via a phase referenceinput 96.

FIG. 9B shows another embodiment of the tool according to the invention,where the tool has a non-conductive pad 5 with a conductive backplate92. The tool also includes the phase sensitive detector 91 adapted tomeasure the amplitude of the voltage that is in phase with the current.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

1. A method for electrically investigating a wall of a borehole in ageologic formation, the method comprising: injecting (71) a current intothe formation at a first position along the wall and returning thecurrent at a second position along the wall, the formation currenthaving a frequency below about 100 kHz; measuring (72) a voltage in theformation between a third position and a fourth position along the wall,the third and fourth positions being located between the first andsecond positions; and determining (73) an amplitude of a component ofthe voltage in phase with the current.
 2. The method of claim 1 furthercomprising: calculating (74) a formation resistivity from the currentand the voltage component that is in phase with the current.
 3. Themethod of claim 2, wherein calculating the formation resistivityincludes applying scalar corrections (75) for current leakage andvoltage inaccuracies.
 4. The method of claim 1, wherein the current isinjected through a source electrode and returned at a return electrode,each of the source and return electrodes being shielded by a conductivebox held at the same electric potential as each electrode, the methodfurther comprising measuring the current.
 5. A method for analyzingborehole logging data, comprising: determining an amplitude of acomponent of a recorded voltage signal in phase with a recorded currentsignal (81), the current signal recorded from a current injected into aformation at a first position along a borehole wall and returned at asecond position along the wall, the voltage signal recorded from avoltage measured between a third position along the wall and a fourthposition along the wall, the third and fourth positions being betweenthe first and second positions.
 6. The method of claim 5 furtherincluding: calculating a formation resistivity (82) using the recordedcurrent signal and the component of the recorded voltage signal in phasewith the recorded current signal.
 7. The method of claim 6 whereincalculating the formation resistivity includes applying a scalarcorrection (83) for current leakage and voltage inaccuracies.
 8. Themethod of claim 5 wherein the recorded current signal is a formationcurrent that is a calculated by subtracting a leakage current from thetotal current, the leakage current being calculated by using anexperimentally determined leakage impedance.
 9. A well-logging tool formaking microelectrical measurements in a borehole, comprising: a padadapted to be placed into contact with a wall of the borehole; a sourceelectrode (2) located on the pad, the source electrode adapted to injectan electrical current into a formation; a return electrode (3) locatedon the pad, the return electrode adapted to receive the electricalcurrent injected by the source electrode; an ammeter operativelyconnected to a circuit including the source and return electrodes; atleast one pair of voltage electrodes (4) located on the pad between thesource and the return electrodes; and a phase sensitive detector (91)operatively coupled to the voltage electrodes and adapted to measure anamplitude of a component of a voltage across the voltage electrodes inphase with the electrical current.
 10. The well-logging tool of claim 9,wherein the pad is comprised of a non-conductive material and furthercomprising: a conductive backplate (92) disposed on a back face of thepad, and covering most of a region between the source and returnelectrodes.
 11. The well-logging tool of claim 9, wherein the phasesensitive detector is operatively coupled to the voltage electrodes andadapted to measure an amplitude of a component of a voltage across thevoltage electrodes in phase with a calculated formation current.
 12. Amethod for electrically investigating a wall of a borehole in a geologicformation, the method comprising: injecting a current into the formationat a first position along the wall and returning the current at a secondposition along the wall, the formation current having a frequency belowabout 100 kHz; measuring a voltage in the formation between a thirdposition and a fourth position along the wall, the third and fourthpositions being located between the first and second positions;calculating a formation current by subtracting a leakage current fom thecurrent; and determining an amplitude of a component of the voltage inphase with the formation current.
 13. The method of claim 12 furthercomprising: calculating a formation resistivity from the formationcurrent and the voltage component that is in phase with the formationcurrent.
 14. The method of claim 13, wherein calculating the formationresistivity includes applying a scalar correction for current leakageand voltage inaccuracies.
 15. The method of claim 12, wherein theformation current is injected through a source electrode and returned ata return electrode, each of the source and return electrodes beingshielded by a conductive box held at the same electric potential as eachelectrode.